Reactive ion scattering from ice in a molecular dynamics perspective

Surface Science 604 (2010) 1135–1142

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Surface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u s c

Reactive ion scattering from ice in a molecular dynamics perspective R.J.W.E. Lahaye Department of Physics, Sungkyunkwan University, Suwon, 440-746, South Korea

a r t i c l e

i n f o

Article history: Received 15 December 2009 Accepted 19 March 2010 Available online 9 April 2010 Keywords: Cs+ Ice Ion scattering Ion–dipole

a b s t r a c t This is a study into the scattering dynamics of the alkaline ions Cs+, K+, Na+, and Li+ from an ice surface, and the process of abstracting water molecules by the scattered ions to form ion–water clusters as a result of the ion–dipole attraction. In a classical molecular dynamics computer simulation a semi-empirical ion–water interaction potential and a modified version of the TIP3P ice model are employed. The thickness of the ice structure at the surface greatly affects the abstraction efficiency. From a thin ice overlayer all alkaline ions exhibit similar scattering probabilities, but Cs+ abstracts water molecules most efficiently; its lower speed facilitates a mechanism where the Cs+ in its outgoing trajectory pulls water molecules out of the ice structure. From a thick ice structure the scattering probabilities decrease dramatically due to an effective energy transfer to the ice structure. A more grazing angle of incidence reduces the energy transfer and enhances the scattering probabilities for the lighter alkaline ions. The deprived formation of ion–water clusters in the simulations confirms that from thick ice the cluster formation probability is reduced by at least three orders of magnitude. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Reactive ion scattering (RIS) is a surface detection technique, which is designed to identify neutral species on surfaces [1–7] and is able to monitor real time dynamics [8,9]. A beam of Cs+ ion projectiles at low incidence energies (10–100 eV) prevents unwanted damage to the surface and the adsorbed species. After the collision with the surface, the scattered ions can pick up neutral species (X) from the surface to form Cs+–X clusters as a result of the ion–dipole attraction; a subsequent mass selective detection of the scattered charged clusters allows an accurate determination of the surface species. Because the alkaline ion has a closed shell electron configuration, it is chemically inert. Therefore processes such as charge transfer are negligible and the interaction with the surface and adsorbates is of physical nature. Research on ice surfaces has gained increasing attention over the past few decades. In higher atmospheric regions ice particles are considered to be an important catalyst of chemical reactions, which are of vital interest to biological systems on Earth; the atmospheric conditions depend for a great part on the existence of ice at high altitudes and in the polar regions, and minute changes have alarming effects on the environmental balance of the atmosphere [10–14]. Recent findings back up a theory that the early development of life has happened in ice or at ice interfaces [15,16]. Ice grains in interstellar regions are of interest to processes which are involved in the formation of protoplanetary disks in dense molecular clouds [17–21].

E-mail address: [email protected]. 0039-6028/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2010.03.028

New challenges arose when ice surfaces became the target of investigation by Cs+–RIS [3,4,6,22]. The preparation of ice interfaces and ice surfaces under laboratory conditions permits Cs+–RIS as a probe for characterizing the chemical properties of microscopic ice particles similar to those in polar, stratospheric, and even interstellar regions [23]. Because the ice surface is rather soft and the Cs+ ion is relatively heavy, surface damage [24] and RIS detection sensitivity are of major concern. Also, the scattering dynamics depends much on the ice thickness, as the flux of scattered ions drops by several orders of magnitude when increasing the thickness of the adsorbed ice overlayers [4]. Nevertheless, experimental results have indicated that these complications do not jeopardize the qualities of Cs+–RIS as a valuable detection technique for ice surfaces [23,25]. Theoretical studies have unravelled essential parts of the RIS scattering dynamics, in particular for Cs+ scattered from metal surfaces [26,27]. In brief, the Cs+–adsorbate cluster formation is most efficient when the projectile scatters away from the surface at a low enough velocity, so that the adsorbate can be dragged along in the outgoing trajectory. The theoretical analysis brought forward novel features, such as the dependence of the abstraction efficiency on the masses of both the adsorbate and projectile. The scattering dynamics from the soft ice structure, however, is too different for simply extrapolating conclusions. In present work I have modeled the RIS scattering dynamics of alkaline ions from an ice surface and weighed the merits of Cs+ ions against K+, Na+, and Li+ as projectile ions. I have employed a classical molecular dynamics simulation, using empirical potentials for the ion–water and for the water–water interactions. Both thick and thin crystalline Ih ice are modelled, where this refers to the relevance of the underlying substrate on which the ice is grown; unlike for thin ice, for

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Table 1 Values of the potential parameters for the water–water interaction of the TIP3P model, for the intramolecular water potential, and for the alkaline ion–water interaction. Units are in Ångström and electronvolts, e is the elementary charge. TIP3P

Alkaline+-H2O

H2O −0.834e + 0.417e 6.597·10− 3 3.5364 14.4

qO qH D ρ

e2 4πε0

R Θ Es Eb

0.9572 104.52 459.55·10− 3 197.7·10− 3

A αCs αK αNa αLi

5000.0 3.3322 3.9598 4.6059 5.1597

thick ice a solid substrate underneath the ice layers has no effect on the surface scattering dynamics. For the scattering dynamics in current work thin ice implies a single bilayer of water molecules supported by a rigid solid, whereas two bilayers are sufficient to simulate thick ice. 2. Computational method The model for the scattering from ice is derived from the existing TIP3P model, which facilitates the conditions for the ice structure. In the next paragraphs I discuss the modifications to this model to accommodate for the ion scattering dynamics in the hyperthermal energy regime (1–50 eV) and introduce a semi-empirical alkaline ion–water potential. 2.1. Ice model The TIP3P model for crystalline Ih ice has been presented and studied by Jorgensen et al. [28]. The water molecules interact with one another via a Coulomb potential between the electric charges at each of the three atoms in the molecule, and a Lennard-Jones type potential between the oxygen atoms. The water–water interaction potential is given in Eq. (1), in which qi, qj, and rij are the charges of, and distances between the atoms in two water molecules. The Lennard-Jones potential between two oxygen atoms has a well-depth D at equilibrium distance ρ. Table 1 lists the values of all parameters. V=


12
6  1 qi qj ρ ρ +D −2 rOO rOO i;j∈fH2 Og 4πε0 rij ∑

ð1Þ

The range of the water–water potential is reduced by multiplying the potentials in Eq. (1) with the switching function [29] of Eq. (2). For x = 2(r− 9.5), this function and its derivatives smoothly drop to zero for r between 9.5 and 10 Å.

f ðxÞ =

8 <

0 ð1−xÞ3 : 1



1 + 3x + 6x2



xN1 0bx b1 : xb0

Fig. 1. A side view of the ice structure with an artistic impression of a scattering trajectory (upper panel) and a top view of the ice structure (lower panel). The active water molecules are black and the fixed water molecules light-gray. This example has two active bilayers of water molecules, with 196 (14 × 14) molecules in each active bilayer. Three bilayers of fixed molecules are underneath and five rows at each side.

ð2Þ

Ice models generally apply periodic boundary conditions to simulate infinite dimensions [30–33]. In case of scattering at hyperthermal energies, a single projectile would cause periodic impact effects on the ice surface, which is undesirable. Instead, the surface of our ice slab has a large enough area of active water molecules, embedded in a structure of rigid water molecules. Fig. 1 shows such an ice structure with two bilayers of active molecules. The rigid molecules never move from their equilibrium positions, as if they have an infinite mass. These fixed molecules provide the long range potential field for the active molecules, cut off by the switching function of Eq. (2). The original TIP3P model treats water molecules as rigid bodies, which requires non-trivial techniques in solving the equations of motion, such as a self-consistent evolution of the rotation-quaternions at each time step [34]. I have streamlined the numerical procedure by adding OH-stretching and HOH-bending degrees of freedom to the active water molecules, taking for granted a somewhat higher demand on computational resources. The interaction potentials for the internal

motions maintain the geometry of the water molecule without affecting the overall dynamics [35]. Harmonic potentials in Eq. (3) are adequate as an approximation of the internal degrees of freedom. The potential parameters are extracted from the energies of the normal vibrational modes in an isolated water molecule [36]. The parameters ks, kb, Es, and Eb are the harmonic constants and energies of the OH-stretching and HOH-bending motions, R is the hydrogenoxygen equilibrium distance, Θ is the equilibrium angle between the two hydrogens with respect to the oxygen, and M represents the masses of the oxygen and hydrogen, according to the subscripts. The values of R and Θ are taken from the water molecule in the TIP3P model. The harmonic potentials were verified by a Fourier analysis of the vibrations in the substrate: the molecule's center of mass vibrates at frequencies between 1 and 5 THz, whereas the intramolecular vibrations are in a higher frequency domain between 15 and 30 THz, similar to observations in experiments [37–39]. VOH ðr Þ

=

ks = VHOH ðθÞ

1 2 k ðr−RÞ 2 s MO MH 2 ðE = ℏÞ MO + MH s

1 2 2 = kb R ðθ−ΘÞ 2

kb =

1 MO MH 2 ðE =ℏÞ 2 MO + MH ð1−cosΘÞ b

:

ð3Þ

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In the ice structure the hydrogen bond between two water molecules is 0.267 eV. The total binding energy of a water molecule in the ice surface is typically between 0.75 and 1.0 eV, depending on the orientations of the surrounding water molecules. The pristine ice structure has the water molecules in their equilibrium positions, resembling an ice crystal at a very low temperature. 2.2. Ion–ice interaction potential The Cs+–water interaction potential is based on the Coulomb interaction between the electrical charges of the TIP3P water molecule and the Cs+ ion. A Born-Mayer type potential between the oxygen and the Cs+ is added to enhance the repulsion at short distances. The total interaction potential between the Cs+ ion and a single water molecule is described by Eq. (4), in which qi is the charge of the atoms in the water molecule, according to the TIP3P model, ri is the distance between the Cs+ and each atom in the water molecule, and rO is the distance between the Cs+ and the oxygen atom. The parameters A and α are derived from a fit to an MP2 ab initio calculation for Cs+–H2O [40]. The attraction is 0.5 eV when the negative oxygen points towards the Cs+ ion. The attractive potential gradually changes into a purely repulsive potential for the reverse orientation. Fig. 2 shows the attractive and repulsive parts of the Cs+–water interaction potential as function of the Cs+–oxygen distance, which nicely overlaps with the data points from the MP2 calculation. V=

1 qi e + A expð−αrO Þ: i∈fH2 Og 4πε0 ri ∑

ð4Þ

The binding energy between a water molecule and the alkaline ions is well known from experimental results [41–44]. The smaller ionic radius causes a stronger bond with the water molecule, which exhibits a linear correlation as illustrated in Fig. 3. Therefore, for Eq. (4) to fit other alkaline ions besides Cs+, only an adjustment to the range parameter α is needed (Table 1 has the different values for α). The attractive and repulsive interaction potentials for all alkaline ions are drawn in Fig. 2. For a lighter alkaline ion, the repulsive wall shifts to a smaller ion–water distance with a larger well-depth. The corresponding well-depths have the same linear dependence as the experimental values, as shown in Fig. 3. This provides a consistent description of the interaction between the alkaline ions and a water molecule.

Fig. 3. The bond strength of the alkaline ion–water potential correlates linearly with the ionic radius. The bond strength of the potential fits in Fig. 2 have the same linear behavior as the experimental data [41–45]. The dotted line is merely a guide to the eye.

2.3. Simulation model Scattering from a thick ice overlayer is simulated by using two active bilayers and the impinging alkaline ion only interacts with the active water molecules. When the projectile penetrates beyond the second active bilayer of water molecules, the trajectory calculation is terminated, assuming the projectile then remains trapped in the ice. For simulating a thin ice film, a single active bilayer of water molecules is used and the rigid water molecules underneath in the second bilayer reflect the ion projectile without energy loss; in this case the alkaline ion interacts with the rigid water molecules through a purely repulsive potential, by using only the Born-Mayer repulsion of Eq. (4) between the projectile ion and the rigid water molecules. This mimics a single ice bilayer grown on top of a more rigid substrate. The ion projectile starts its trajectory at 25 Å above the ice surface, with a random impact parameter in the center of the active area of the surface. A scattering event occurs when the ion has bounced off the surface and reaches again a distance of 25 Å above the surface. The statistics on the scattering events are then reported irrespective of outgoing angles. The trajectories, which result in sticking or trapping, are one of three cases: the ion traverses horizontally along the surface and reaches one of the edges of the active area, penetrates beyond the second bilayer, or otherwise consumes over 1.5 ps since the moment of impact on the surface. Scattering probabilities are calculated as the total number of scattered species divided by the total number of impacting Cs+ ions. The results are thus independent of the incoming Cs+ flux in experiments for as long as the ion flux is low enough so that Cs+ impacts can be considered as isolated events (disjoined from possible adjacent impacts). The Numerov-Verlet integration procedure [34] is used to solve the equations of motion and a time step of 1 fs keeps total energy conserved within a percent. Typically 600 trajectories were calculated for a single data set. The ice model used in current work mimics a temperature condition close to zero Kelvin. At a finite temperature thermal fluctuations in the ice are much smaller than the kinetic energy range of the impacting Cs+ ions. The scattering dynamics is therefore not sensitive to temperature effects. 3. Results

Fig. 2. Interaction potentials between a water molecule and alkaline ions. Both solid and dashed lines correspond from left to right to the alkaline ions Li+, Na+, K+, and Cs+ respectively. The potentials have an attractive well when the oxygen of the water molecule points towards the positive ion (solid lines), whereas the potentials are purely repulsive for the reverse orientation of the water molecule (dashed lines). The thick dots on the curves are the energies from an MP2 ab initio calculation for the Cs+–water potential.

3.1. Scattering from thin ice At first I have investigated the alkaline ion scattering from a single bilayer of active water molecules. The impinging ion projectiles exchange energy only with the active water molecules, whilst the rigid

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water molecules underneath reflect the projectiles without energy loss. This resembles a thin ice layer grown on top of a more robust solid such as Platinum or Ruthenium. The incidence angle of the projectile ions is 45 ° and the scattered species are collected irrespective of outgoing angle. The scattering probabilities are calculated as the ratio of the number of scattered species and the total number of incidence projectile ions. The scattering probabilities as function of the Cs+ incoming energy are shown in Fig. 4 for scattered unclustered Cs+ and for Cs+–water clusters. There is a scattering threshold between 5 and 10 eV, because below 10 eV efficient energy transfer to the active water molecules causes trapping of the impinging Cs+. This trapping diminishes at higher incoming energies, leading to a gradual increase of the scattering probabilities with increasing incidence energy. The scattering of unclustered Cs+ shows a steady increase, whereas the Cs+–water clusters exhibit a maximum at 20 eV and then decreases for higher energies. Although there is an abundance of scattered Cs+ for incidence energies above 20 eV, the higher energy apparently hampers the Cs+– water cluster formation. The maximum at 20 eV indicates that if the outgoing Cs+ is too fast, it becomes more difficult to pick up one or more

water molecules, due to the inertia of the water molecule [27]. The probability distribution with respect to cluster size is shown in Fig. 5 for four selected incidence energies. The probability decreases with increasing cluster size, in line with experiments which show that scattered Cs+ projectiles have difficulties with forming larger Cs+–water clusters [4]. Fig. 5 also indicates that the Cs+–water clusters never contain more than six water molecules. At a first glance, the absence of larger cluster sizes could appear as an artifact of our analysis of the final simulation results. In this analysis, the competition between the attractive part of the interaction potential and the rovibrational energy between the Cs+ and each water molecule determines whether or not the water molecules remain attached to the Cs+. This may overlook events where the Cs+ pulls a long string of water molecules out of the ice structure, which may result in water clusters with more than six water molecules. However, I have watched carefully numerous animations of scattering events and such string formations never occurred, probably due to the weak binding energy beyond the first hydration shell of the Cs+ ion. It is therefore valid to conclude that Cs+–water clusters are formed by water molecules only occupying positions in the first hydration shell around the Cs+ ion, similar to gas phase results on the formation of Cs+–water clusters [42,43]. Hence, the maximum of six water molecules attached to the Cs+ reflects the symmetric octahedron arrangement of water molecules, which balances the attractive and repulsive forces between the water molecules and the Cs+ in the center of the cluster. Fig. 6 shows the average velocity of the scattered species as function of the incoming Cs+ energy. From a threshold of 5 eV, all velocities gradually increase with lower velocities for the larger clusters. If its outgoing velocity is too fast, scattered Cs+ cannot pick up water molecules. Therefore unclustered Cs+ ions scatter with the highest average velocity, and the slower the scattered Cs+, the easier it can pick up more water molecules. The same trend has been observed for Cs+ picking up water molecules adsorbed on a Pt(111) surface [4]. These observations are a clear illustration that the velocity of the scattered ion, rather than its kinetic energy, is the critical factor in the cluster formation [27]. As an aside, I should acknowledge that for Fig. 6 the error bars of the averaged velocities (not shown in the figure) are rather large with substantial overlap between the curves. This large statistical variation of the cluster velocities is caused by two effects. At first, a well oriented water molecule (with the negative O-end pointing towards the Cs+) attaches easier to a faster outgoing Cs+, than a less ideally

Fig. 5. Probability of the formation of the scattered Cs+–water clusters (from Fig. 4) as function of cluster size for four Cs+ incoming energies.

Fig. 6. Averaged final velocities of scattered Cs+ and Cs+–water clusters as function of incoming Cs+ energy with 45° incidence angle. The connecting lines are merely guides to the eye. The unit of time τ on the velocity axis is 10.2 fs.

Fig. 4. The scattering probabilities from a thin ice film as function of the Cs+ incoming energy at an incidence angle of 45°. The scattered ions are Cs+ (open symbols) and Cs+–water clusters (solid symbols). The scattered ions are collected irrespective of outgoing angle.

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oriented water molecule, that needs to be re-oriented during the cluster formation. Secondly, the outgoing Cs+ can pull either one water molecule after another out of the ice structure, or at once several water molecules; the mass of the water cluster in the last mechanism requires a slower outgoing Cs+. As a result, the same cluster sizes can be formed by a variety of outgoing velocities, which gives rise to a relatively large statistical variation in the velocities. Nevertheless, the general trends of Fig. 6 demonstrate that the larger Cs+–water clusters require a slower outgoing Cs+. The water molecules give easily way to an impacting Cs+ projectile, because of the weak binding energy between water molecules in ice, and even more so because of the heavy mass of the Cs+ projectile. The result is a severe damage to the ice surface, where Cs+ impacts create crater-like holes with a typical radius of 10 to 20 Å. Given that the Cs+ projectile is more than seven times the mass of a water molecule, a less violent collision dynamics is expected for lighter projectile ions. To this end, I have simulated ice scattering with K+, Na+, and Li+, and investigated the ion scattering and ion– water cluster formation process. Fig. 7 contains the probabilities for scattered ions and ion–water clusters from a thin ice film for Cs+, K+, Na+, and Li+ projectiles as function of the incidence energy. The scattering dynamics is dominated by the interaction with the solid underneath the single bilayer of water molecules, which in our model recoils all impacts without energy loss. Therefore the scattering probabilities as function of incoming energy for unclustered ions in Fig. 7a are more or less the same for all alkaline ions, with a similar linear increase from a threshold between 5 and 10 eV. Note that the scattering threshold slightly shifts to a higher energy for the smaller ions, due to their stronger bond with the ice surface, as a consequence of the different molecular bonds in Fig. 3. The ion–water cluster formation in Fig. 7b shows a remarkable difference between Cs+ and the other alkaline ions. The pronounced maximum at 20 eV in the scattering probability for Cs+ (same data from Fig. 4) is not at all

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Fig. 8. Averaged final velocity of the scattered K+ and K+–water clusters from a thin ice film at 45° incidence angle, as function of incidence energy of the K+. The lines are merely guides to the eye. The time τ is 10.2 fs.

present for K+, Na+, and Li+. Furthermore, the ion–water clusters show a severely reduced scattering probability, which even becomes negligibly small for the Li+ projectiles. An important reason for the low probability of the cluster formation with the lighter projectile ions, is the higher velocity; at equal energies the speed of K+ is about twice that of Cs+, whereas Li+ is even four times as fast. This effect of the ion velocity on the cluster formation is shown in Fig. 8 for K+. The velocity of the unclustered K+ increases steadily with incidence energy. The flat velocity distribution of the K+–water clusters for incidence energies above 15 eV shows that the clusters can only be formed by outgoing K+ ions below a critical speed. The pick-up of two water molecules requires an even lower velocity of the outgoing K+ projectile than for picking up a single water molecule. A scattered K+ projectile does not pick up more than two water molecules, because its outgoing velocity is too high for this to occur. In conclusion, for the scattering from thin ice the projectile ions impact on a single ice bilayer with a rigid structure underneath. If the incidence projectile has a relatively large momentum normal to the surface and provided the underlying solid substrate has good scattering properties, then scattering probabilities are high, as shown in Fig. 7a. The velocity of the scattered projectile ions determines the efficiency of picking up water molecules in the outgoing trajectory. Because Cs+ has the lowest velocity due to its high mass, it also has the best conditions for picking up water molecules with a maximum for the formation of ion–water clusters at an incidence energy of 20 eV. 3.2. Scattering from thick ice

Fig. 7. Scattering probability of the alkaline ions (a) and ion–water clusters (b), both as function of the alkaline ion incidence energy. Angle of incidence is 45°.

Under laboratory conditions, ice is usually grown layer by layer on a solid substrate such as a Ruthenium or Platinum surface [4,46]. “Thick ice” then refers to the condition that the scattering dynamics from the ice overlayer is not affected by the supporting substrate. This is achieved by utilizing an ample number of ice bilayers. A penetration depth of two or three bilayers causes the projectiles to lose a substantial amount of their initial kinetic energy and such projectiles are deemed to get trapped in the ice. For simulating thick ice, I may therefore implement just two bilayers of active water molecules in the ice substrate. The impinging projectile ion only interacts with the active water molecules. Projectile ions can be reflected at the ice either from the first or the second active bilayer of the surface; the trajectory is terminated when the projectile penetrates beyond the second bilayer of

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Fig. 9. Probabilities of the scattered (open symbols) and trapped (solid symbols) alkaline projectile ions from a thick ice film as function of the incidence energy of the ions for two incidence angles, 45° and 60°.

active water molecules, assuming that such trajectories inevitably lead to implantation into the bulk of ice. Projectile ions penetrate easily into the ice substrate, but for a grazing angle of incidence the smaller perpendicular momentum of the impinging ion can reduce the penetration depth. I have therefore investigated incidence angles of 45° and 60°, with respect to the surface normal. Two key-properties determine the characteristics of alkaline ion scattering from thick ice: the scattering probability, i.e. moving away from the surface after impact, and the trapping probability (so that the sum of the two probabilities is unity). Fig. 9 presents the two properties as function of incidence energy. For 45° incidence, only the Li+ projectiles show a significant amount of scattering, up to about 20% at 40 eV. The other alkaline ions, Cs+, K+, and Na+, get mostly trapped in the ice for all incidence energies. A Li+ can undergo direct recoil from the surface water molecules, because its mass is less than half of a single water molecule. The scattering probability of the Li+ projectiles increases with incidence energy, because an excess of kinetic energy helps overcome the strong bond with the ice surface. At 45° incidence trapping in the ice dominates the scattering dynamics for all alkaline ion projectiles. The momentum component perpendicular to the surface is responsible for the high penetration probability. A more grazing angle of incidence reduces the perpendicular momentum in favor of the parallel momentum along the surface. This angular effect is shown in Fig. 9 for 60° incidence. For Cs+ the change of incidence angle has little effect and the vast majority of the trajectories penetrate into the ice. However, for the other alkaline ions the grazing incidence indeed enhances the scattering probabilities, especially at the higher incidence energies, to about 20 to 25% scattering at 40 eV incidence energy. The Li+ projectile has again the best overall scattering probabilities. The heavier ions K+ and Na+ can scatter away from the surface after subsequent multiple collisions with the water molecules in the ice surface. For 45° incidence only Li+ can scatter away from the surface, but none of the scattered Li+ pick up water molecules. For 60° incidence the scattering probabilities of Li+, Na+, and K+ are better, but even then the probability for forming ion–water clusters is under a percent, which is very small when considering the strong attraction between these alkaline ions and a water molecule. The velocities of the scattered projectile ions can give a clue as to why the pick-up probabilities are so low, despite the reasonable scattering properties. Fig. 10 shows the average velocities of the scattered ions in the case of 60° grazing incidence. The velocities increase with increasing incidence energy, with Li+ by far the fastest outgoing projectile. The velocities of the outgoing Li+ and K+ projectiles are always higher than those of ion–water clusters produced from thin ice, namely about 0.25 Å/τ in Figs. 6 and 8. Apparently from thick ice too few ions scatter at slow enough outgoing velocities to be able to pick up water molecules. Ion scattering at grazing incidence from thick ice then produces either ions trapped in the ice structure, or fast outgoing

Fig. 10. Averaged outgoing velocities as function of incidence energy for the alkaline ions Li+, Na+, and K+, scattered from thick ice at 60° incidence. For Cs+ no scattering occurs and it is therefore not shown. The time τ is 10.2 fs.

scattered ions. In that case water molecules cannot “follow” the fast scattered ions. The absence of Cs+ scattering from thick ice requires a careful interpretation. With 600 trajectory simulations per data set, the lowest scattering probability is accurate down to 1/600 ≈ 10− 3. So at most the conclusion can be that the scattering probability is less than 10− 3. The probability of forming Cs+–water clusters must be even smaller. For such low probabilities the thus far neglected aspects in the model may become important. For example, it might be necessary to simulate a larger surface area so that the ions can travel longer distances, or define a better criterion for trapping events. The scattering dynamics will also be more sensitive to imperfections in the ice structure or to temperature effects. I have not augmented the model in order to include scattering events of extreme low probabilities, because the simulation results are already qualitatively in line with experimental findings, which also report equally low probabilities for the scattering and cluster formation from thick ice [4]. In stark contrast to the scattering from thin ice, the Cs+ projectiles scattered from thick ice produce very low probabilities for both plain scattering and for pick up of water molecules in RIS. For lighter ion projectiles one might expect slightly better scattering and water abstraction conditions, especially at grazing incidence angles. However, even under best conditions the probability of abstracting water molecules is still several orders of magnitude smaller than for optimal scattering from a thin ice overlayer. 4. Conclusions The collision dynamics of alkaline ion projectiles with an ice surface turns out to be rather complex. The impinging projectile collides with several water molecules at high energy exchange rates, because the water molecules easily give way and, like a sponge, absorb a significant part of the kinetic energy. The consequent chaotic process obscures a simple collision dynamics picture. General trends emerge from the analysis of a few thousand trajectories. In conclusion I highlight important aspects relevant to the alkaline ion–ice interaction in order to clarify the RIS scattering dynamics at the ice surface in the light of the formation and scattering of alkaline ion–water clusters. The interaction time with the water molecules upon impact of the ion projectiles is long enough for the water molecules to absorb a large amount of kinetic energy, while at the same time this energy is cascaded to adjacent water molecules in the ice structure (very different from the simple binary collisions which dominate the dynamics in the keV energy regime). Therefore an ion, which impacts

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on a thick ice structure, interacts simultaneously with 20 or more water molecules. The result is a severe energy loss of the ion projectile within the top most two bilayers of the ice surface and considerable damage to the surface ice structure. This results in a high trapping probability, unless a more solid substrate underneath a thin ice layer reflects the impinging projectiles. For Cs+–RIS from ice surfaces, the large mass mismatch between a water molecule and the ion is prominent, but the dynamics is affected even more by the weak binding energy between the water molecules in ice. For example, a water molecule and a Si atom have similar small masses, but Cs+–RIS experiments from a Si(111) surface have revealed high scattering intensities [1]. The Si substrate atoms make a collective recoil due to the strong Si-Si binding energy of several eV's, whereas the bond between water molecules in ice is merely a quarter of an electron volt. The ice surface is soft, which permits water molecules to be pushed aside easily by incoming projectiles without an effective collective recoil [29]. An impinging ion can easily push water molecules away from their original lattice positions, while the water molecules carry away a considerable portion of the incidence energy of the ion. A rather explosive scattering dynamics occurs creating many “loose” water molecules, which can participate in the abstraction process. A slow enough Cs+ ion projectile can then attract efficiently several water molecules in its outgoing trajectory. For ions lighter than Cs+ the mass ratio between the projectile ion and a water molecule also affects the scattering dynamics. Although a binary collision overly simplifies the dynamics picture, it is a useful means of understanding the energy transfer. Eq. (5) expresses the relative energy change of the projectile, where μ is the mass ratio of the two colliders and θi is the impact parameter's angle with respect to a head-on collision. ΔE 4μcos2 θi = : Ei ðμ + 1Þ2

ð5Þ

In a full head-on collision (θi = 0), the energy transfer ΔE (=Ei − Ef) approaches total energy loss when the mass ratio μ gets close to one. Since the energy loss can be reduced by changing the impact parameter (θi ≠ 0), a light alkaline ion projectile can be reflected from the ice surface in two or more grazing collisions. Such a trajectory gradually bends its path and moves away from the surface with relatively high energy. Trajectories of this kind explain the scattering and high outgoing velocities of Li+, Na+ and K+ at 60° incidence. A stronger ion–dipole attraction between the projectile ion and a single water molecule would enhance the ion–water cluster formation, were it not that the collective attraction by the ice structure also creates a stronger bond between the ion and the surface. For example, the K+–water cluster has a binding energy of 0.9 eV and the adsorption energy on the surface is about 2 eV. The high adsorption energy hampers the ions to scatter away from the surface at low incidence energies. Whether ions scatter from the ice surface or not depends on the scattering threshold of the incidence energy, which typically varies from 5 to 15 eV. The successive ion–water formation is only possible by scattered ions, which have a slow enough velocity to pull one or more water molecules along in their outgoing trajectory. Therefore both the incoming energy and the outgoing velocity are critical factors in the water abstraction probability. From a thin ice overlayer Cs+ projectiles exhibit the best properties for both scattering and water abstraction through RIS, because all of the afore mentioned criteria contribute positively. Moreover, the heavy Cs+ projectiles easily cut through a thin ice layer, lose some energy in the process, and scatter from the solid structure underneath. At a specific incidence energy (20 eV in our case) the velocities of the scattered Cs+ projectiles are optimal for water abstraction from the ice overlayer. For lighter alkaline ions, on the other hand, the velocities of

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the scattered projectiles are too high for an efficient abstraction of water molecules. For grazing incidence angles from thick ice, however, the scattering probabilities for Cs+ become much smaller than those for the lighter ion projectiles. The use of K+ or Na+ may therefore enhance RIS in experiments with thick ice. The simulation results explain a number of observations in the experiments. First of all, a high efficiency for Cs+–RIS has been observed in case of a thin overlayer of H2O [4,5,22,47]. Second, if the scattering conditions are good (such as scattering from a thin ice layer on top of a metal solid), then Cs+ is the preferred candidate for RIS experiments [1,48]. Third, the velocity of the scattered Cs+–water clusters depends on the size of the cluster: the more water molecules abstracted by the Cs+, the slower the speed of the cluster [4]. And finally, the RIS efficiency dramatically collapses for thick ice overlayers [4]. The agreement of general trends between experiment and simulation vindicates the ice and molecular dynamics model to be a valuable tool to mimic RIS from an ice surface. 5. Summary I have applied a classical molecular dynamics model to the scattering of alkaline ions from an ice surface and the subsequent formation of ion– water clusters by reactive ion scattering (RIS). Scattering from a thin ice layer at 45° incidence shows that Cs+ has the highest RIS efficiency, because its low speed in the outgoing trajectory promotes the water attachment. The mechanism of Cs+ ions pulling water molecules away from the ice structure in their outgoing trajectory is evidenced by a pronounced maximum in the RIS probability at 20 eV incoming energy. The lighter alkaline ions K+, Na+, and Li+ have similar scattering properties as Cs+ from thin ice, but their RIS probabilities to form ion– water clusters are much lower without exhibiting a maximum. The scattering probabilities reduce by several orders of magnitude when the ice surface consists of 2 bilayers or more, because the majority of projectiles get trapped in the ice structure. Better scattering properties exists for grazing incidence angles, but only improve appreciably for the scattering of K+, Na+, and Li+. Although all alkaline ions show a very low RIS efficiency from thick ice, K+ and Na+ perform slightly better at picking up water molecules. The simulation results presented here are in good agreement with experimental findings and the model is therefore useful to illustrate a molecular dynamics picture, which describes the complex scattering phenomena of ions impacting on an ice surface. Acknowledgments I am grateful to prof. Heon Kang of Seoul National University for the stimulating discussions. I also thank prof. Sangyoub Lee of Seoul National University for providing additional computer facilities. References [1] M.C. Yang, C.-H. Hwang, H. Kang, Journal of Chemical Physics 107 (1997) 2611. [2] H. Kang, K.D. Kim, K.Y. Kim, Journal of American Chemical Society 119 (1997) 12002. [3] S.-C. Park, K.-W. Maeng, T. Pradeep, H. Kang, Nuclear Instruments and Methods in Physics Research B 182 (2001) 193. [4] J.R. Hahn, C.-W. Lee, S.-J. Han, R.J.W.E. Lahaye, H. Kang, Journal of Physical Chemistry A 106 (2002) 9827. [5] S.-J. Han, C.-W. Lee, H. Yoon, H. Kang, Journal of Chemical Physics 116 (2002) 2684. [6] S.-C. Park, K.-W. Maeng, H. Kang, Chemistry - A European Journal 9 (2003) 1706. [7] K.-Y. Kim, J.-H. Kim, J.-H. Cho, L. Kleinman, H. Kang, Journal of Chemical Physics 118 (2003) 6083. [8] J.-H. Kim, R.J.W.E. Lahaye, H. Kang, Surface Science 601 (2007) 434. [9] C.-W. Lee, P.-R. Lee, R.J.W.E. Lahaye, H. Kang, Physical Chemistry Chemical Physics 11 (2009) 2268. [10] M.J. Molina, T.-L. Tso, L.T. Monina, F.C.-Y. Wang, Science 238 (1987) 1253. [11] S. Solomon, R.R. Garcia, S.F. Rowland, W.D.J., Nature 321 (1986) 755. [12] D.W. Fahey, K.K. Kelly, G.V. Ferry, L.R. Poole, J.C. Wilson, D.M. Murphy, M. Loewenstein, K.R. Chan, Journal of Geophysical Research 94 (1989) 11299. [13] G. Kroes, D.C. Clary, Geophysics Research Letters 19 (1992) 1355.

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